逆极限以及双重逆极限空间中利普希次跟踪性和几乎周期点的研究  

Lipschitz Shadowing Property and Almost Periodic Point on the Inverse Limit and Double Inverse Limit Spaces

作　　者：冀占江 陈占和[4] 张更容 JI Zhanjiang;CHEN Zhanhe;ZHANG Gengrong(School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,China;Guangxi Colleges and Universities Key Laboratory of Professional Sofiware Technology,Wuzhou Universin,Wuzhou 543002.China;Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Wiuzhou University,Wuzhou 543002,China;College of Mathematics and Information Science,Guangxi University,Nanning 543004,China;School of Mathematics and Computational Science.Hunan First Normal University,Changsha 410205,China)

机构地区：[1]梧州学院大数据与软件工程学院,广西梧州543002 [2]梧州学院广西高校行业软件技术重点实验室,广西梧州543002 [3]梧州学院广西高校图像处理与智能信息系统重点实验室,广西梧州543002 [4]广西大学数学与信息科学学院,广西南宁5430004 [5]湖南第一师范学院数学与计算科学学院,湖南长沙410205

出　　处：《山西大学学报（自然科学版）》2022年第2期343-347,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11461002);广西自然科学基金(2020JJA110021);湖南省自然科学基金(2018JJ2074);梧州学院校级重点项目(2020B007)。

摘　　要：在逆极限空间中研究了利普希次跟踪性的动力学性质,得到移位映射具有利普希次跟踪性当且仅当自映射了具有利普希次跟踪性。将逆极限空间中几乎周期点的定义引入到双重逆极限空间,并研究了它的拓扑结构,得到移位映射的几乎周期点集等于自映射在其几乎周期点集上形成的双重逆极限空间。从而推广了逆极限空间中跟踪性和几乎周期点的结果。The dynamical properties of Lipschitz shadowing property are studied in the inverse limit space,it is shown that the shift map has the Lipschitz shadowing property if and only if the self-map has the Lipschitz shadowing property.Moreover,the definition of almost periodic point in the inverse limit space is introduced to the double inverse limit space and its topological structure is studied.It is shown that almost periodic point sets of the shift map is equal to the double inverse limit space of the self-map in the almost periodic point sets.The results of shadowing property and almost periodic point are generalized in the inverse limit spaces.

关 键 词：双重逆极限空间 逆极限空间 利普希次跟踪性 几乎周期点 

分 类 号：O189.11[理学—数学]